Preheat oven to 425Â°.
Combine first 7 ingredients, then set aside.
Place the sliced apples in a large bowl. Whisk together the cornstarch, cinnamon, allspice, nutmeg, ginger, and sugar, then pour over the apples and gently toss to coat. Turn the apples out into a large, oven-proof skillet, then pour the apple juice over top.
Gently spread the crumble mixture over the top of the apples, then place in the oven and bake for 20 minutes, or until the apples are soft and the crumble mixture is golden brown. Remove from oven.
Warm the cream cheese icing in the microwave, in 15 second intervals until thinned and smooth. Pour over the crisp, then serve immediately.